Unformatted text preview: the receiver of the message uses “majority” decoding, what is the probability that the message will be incorrectly decoded? What independence assumption are you making? (By majority decoding we mean that the message is decoded as “0” if there are at least 3 zeros in the message received and as “1” otherwise.) Problem 4 Let X be a binomial random variable with parameters n and p . (a) Show that P ( X = k + 1) = p 1p nk k + 1 P ( X = k ) , k = 0 , 1 ,...,n1 . (b) As k goes from 0 to n , P ( X = k ) ﬁrst increases and then decreases. Show that this probability reaches its largest value when k is the largest integer less than or equal to ( n + 1) p . The following problem is optional for 3500 students, mandatory for students enrolled in 5500 Problem 5 If X has a Poisson( λ ) distribution, then ﬁnd E [ X ( X1)( X2) ··· ( Xk )]. 1...
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 Summer '08
 WEBER
 Central Limit Theorem, Normal Distribution, Probability theory, Charles, binomial random variable, standard normal density

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